Re: In the rectangular coordinate system shown, points A and E [#permalink]
23 Apr 2018, 01:50

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In the line \(AB\) by visualization point \(A\) is \((x,0)\). and point \(B\) is \((0,y)\)

Since the given point \(c(-3,5)\) is the mid-point of the line we can make a eqn \(x + 0/2 = -3\) or, \(x = -6\)

\(\frac{y + 0}{2} = 5\)therefore \(y = 10\)For line \(AB\) \(A(-6,0) B(0,10)\)Now, we can similarly calculate the value of point \(D\) and \(E\) in the line \(DE\)Point \(D(0,y)\) and point \(E(x,0)\)Hence, \(\frac{0+x}{2} = 3 or x = 6\)\(\frac{y+0}{2} = -5\)or, \(y=-10\)For line \(DE\) D(0,-10) and \(E(6,0)\)

when we have two points we can calculate the slope for each line AB and DE we have three set of points so we can calculate slopeFor the line \(AB\) slope \(= \frac{10-0}{0-(-6)} = \frac{10}{6} = \frac{5}{3}\)For the line \(DE\) slope \(= \frac{0-(-10)}{6-0} = \frac{5}{3}\)option c
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes